In addition to lens opening and how close you are to your subject, the size of the sensor affects depth-of-field.
Most digital cameras have more depth-of-field than 35mm film cameras.
Most digital SLR cameras have sensors that are smaller than 35mm film.
Therefore, they have more depth-of-field than film cameras.
When using f/8 with a digital SLR, there's more depth-of-field than when you use f/8 with a 35mm film camera.
You can't blur backgrounds as much with digital SLRs.
But more is in focus when doing close-up (macro) photography.
If you use a point-and-shoot camera, you can ignore the discussion about depth-of-field.
Your camera has a sensor that's very small.
Therefore, your camera has lots of depth-of-field—even at wide lens openings.
Having lots of depth-of-field is both good and bad.
The #1 complaint of photographers is unsharp photographs.
With lots of depth-of-field, your photographs will be sharp.
This is especially useful when doing close-up (macro) photography, where there is less depth-of-field because you're close to the subject.
You're less able to blur the background behind the subject.